The design of imaging optics is a centuries-old art with literally thousands of inventions in the prior art. Nearly all of these are combinations of flats and spherical surfaces, due to their relative ease of manufacture. Surfaces with substantial departure from sphericity are known as aspherics, but aside from known quartic shapes such as the ellipsoid and the paraboloid there was little use of aspheres until the twentieth century, when advances both in theory and fabrication technology brought them into prominence. Aspheric surfaces can advantageously substitute for multiple spherical surfaces, resulting in less costly devices, even if a single asphere is more costly than a sphere. With the advent of injection-molded plastic optics and precision molded glass optics, aspheres entered the optical-technology mainstream.
Applications of aspheric optics fall into two categories, imaging and non-imaging. Non-imaging optics is concerned with illumination and the distribution of optical power, with the defining constraint being the behavior of only the outermost rays (called edge rays) of a flux distribution. Imaging optics, however, is concerned with the spatial modulation of flux, with the goal of reproducing a particular flux distribution (the object) at another location (the image). Nonimaging optical design need only take care of the edge rays, a relatively small portion of all rays, but an imaging system must send all rays to their appropriate destination, parameterized by the system magnification m. A ray originating at coordinate point (x,y) on the object must arrive at the image coordinate (mx, my), known as the image-mapping requirement. In the real world of imaging each point on the object typically radiates flux in all forward directions (i.e., nearly hemispherically) and practicality demands that a significant percentage of this flux reach the proper image point, with little or none going anywhere else on the image plane, once it enters the optical system aperture. In the world of theory, however, many aspheric design procedures hold only when rays hitting a surface subtend only a small solid angle, near the surface normal, and relatively parallel to the optical axis. This enables approximate aberration coefficients to be rapidly calculated for aspheric surfaces in design optimization.
Attaining perfect image mapping for every object point would theoretically require an infinite number of surfaces, but with a limited number of surfaces, state of the art techniques define a merit function to evaluate deviations from ideal imaging in order to minimize loss of image formation over sampled points of the image plane.
A general difficulty with aspherics is that they generally do not have a closed form solution for ray intersections, unlike the algebraic ease with which intersections are calculated for flats, spheres, and the other quadric surfaces (torus, cylinder, ellipsoid, paraboloid, hyperboloid), enabling optimal designs to be derived just with a formula. Aspheres in general, however, generally require a computationally intense iterative search that closes in on the precise intersection.
State of the art imaging optics design is done via optimization techniques using a parametric representation of a selected group and type of optical surfaces. A merit function of those parameters is defined and the search for the optimum of the merit function is done by a computer-aided multiple-parameter algorithm. The implementation of this algorithm may be based on different techniques, as binned least-square methods, simulated annealing, genetic algorithms, etc. However, the differentiation between local and global optimum is not guaranteed, and the optimization depends for its success upon the particular mathematical representation chosen to specify the surfaces. Moreover, usually the optimum found is not too far from the initial guess of the designer, so solutions far from that guess are not accessible in practice. In this application some of the embodiments refer to wide angle projection optics using one mirror. Devices for such an application also including mirrors are disclosed in prior art patents as U.S. Pat. Nos. 6,771,427 and 6,612,704 and US Patent Application No. 2001/0050758 A1. All of them have been obtained by the use of standard optimization procedures.
The only cases in prior art where no optimization is done are based on problems stated in terms of ordinary differential equations. This is the case of the single surface designs to provide axial stigmatism (that is, correction of spherical aberration of all orders), as Cartesian ovals or Schmidt correctors, and the case of the two aspheric surface aplanatic designs, as those by Schwarzschild in 1905 for 2 mirrors (see Born & Wolf, Principles of Optics, p. 168).
Earlier versions of a simultaneous multiple surface (SMS) method for designing optical devices were disclosed in U.S. Pat. Nos. 6,639,733 and 6,896,381 and US Patent Application No. 2005/0086032. This design method generates surfaces locally, based on their refraction of the relevant rays incident upon them. However, the earlier versions of the SMS method disclosed in those patent documents were directed to non-imaging optics and for rotationally symmetrical optics they are restricted to the use of meridional rays, while the present application discloses constructive methods using skew rays.
SMS methods for designing imaging optics were discussed in published reports on two projects: “Televisión por proyección ultra-delgada de pantalla grande y alta resolución” (Television by ultra-thin, high-resolution projection on a large screen) (Financer Entity: Ministerio de Ciencia y Tecnología [Ministry of Science and Technology of the Kingdom of Spain] referencia TIC2001-3617-C02) and “Sistemas ópticos avanzados para displays de proyección (Advanced optical systems for projection displays)” (Financer Entity: Ministerio de Ciencia y Tecnología [Ministry of Science and Technology of the Kingdom of Spain] referencia TEC2004-04316), as well as the doctoral thesis “Sistemas ópticos avanzados de gran compactibilidad con aplicaciones en formación de imagen y en iluminación” (Ultra-compact advanced optical systems for image formation and illumination applications), all by: Fernando Muñoz and Pablo Benítez. These concepts comprise procedures to design optical devices for imaging applications, particularly wide angle projectors.
However, those previous publications by Dr. Muñoz and Benitez do not disclose good calculation procedures for the application of the SMS-imaging design method, particularly no constructional algorithm for skew rays has hitherto been published. Therefore, a skilled person in the field cannot reproduce the designs from the aforementioned publications by Dr. Muñoz and Pablo Benitez. Additionally, the designs in those previous publications did not consider the possibility of both the object and the input pupil being decentered relative to the optical axis of the optical surfaces to be designed, while the present application does address that possibility. This case is valuable, particularly in mirror based designs, to solve problems of shading and obstruction in practical cases.